How Does Molecular Diameter Correlate with the Penetration Barrier of Small Gas Molecules on Porous Carbon-Based Monolayer Membranes?

Molecular diameter is an essential molecule-size descriptor that is widely used to understand, e.g., the gas separation preference of a permeable membrane. In this contribution, we have proposed two new molecular diameters calculated respectively by the circumscribed-cylinder method ( D n ' ) and the group-separated method ( D n ), and compared them with the already known kinetic diameter ( D k ), averaged diameters ( D pa ), and maximum diameters ( D pm and D mm ) in correlating with the penetration barriers of small gas molecules on a total of 14 porous carbon-based monolayer membranes (PCMMs). D 1 ' and D 2 ' give the best barrier-diameter correlations with average Pearson's correlation coefficients of 0.91 and 0.90, which are markedly larger than those (0.77, 0.76, 0.60, 0.48, 0.33, and 0.32) for D 1 , D 2 , D k , D pa , D pm , and D mm . Our results manifest that the choice of vdW radii set does not drastically change the barrier-diameter correlation. Our newly defined D 1 ' , D 2 ' , D 1 , and D 2 , especially D 1 ' and D 2 ' , show universal applicability in predicting the relative permeability of small gas molecules on different PCMMs. The circumscribed-cylinder method proposed here is a facile approach that considers the molecule's directionality and can be applicable to larger molecules. The excellent linear correlation between D n ' and gas penetration barrier implies that the computationally less demanding molecular diameter D n ' can be an alternative to the penetration barrier in diagnosing the gas separation preference of the PCMMs.